Tarim basin mainly composed of desert regions is an important oil and gas exploration area. The desert seismic data acquired from Tarim basin is often characterized by low Signal-to-Noise Ratio (SNR) ; also, the effective signals and noise seriously overlaps in low-frequency domain. These two points bring numerous difficulties to the denoising of desert seismic data, so as to affect the following inversion, imaging, and interpretation. In order to suppress the background noise effectively and recover the effective signals completely, we adopt the basic strategy of Generative Adversarial Network (GAN) and then utilize a denoiser to replace the generator of GAN, so as to propose a novel denoising network for the desert seismic data, named Desert Seismic Convolutional Adversarial Denoising Network (DSCA-Net). In DSCA-Net, we propose a novel loss function by combining the mean square error loss and adversarial loss. Then, this loss function is used to optimize the network parameters of DSCA-Net, so as to obtain the denoising model aiming at the desert seismic data. Synthetic and real experiments show that (1) the proposed DSCA-Net can effectively suppress the desert background noise and significantly enhance the continuity of events ; (2) after processed by DSCA-Net, the signal-to-noise ratio of desert seismic data is obviously improved.